.
Find the general solution √3cosx+sinx=1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
=
.
Multiply both sides by
. You will get
=
. (1)
Notice that
=
,
=
.
Substitute it into the left side of (1). You will get
=
. (2)
Apply the formula sin(a)*cos(b) + cos(a)*sin(b) = sin(a+b) to the left side of (2). You ill get
=
. (3)
It implies
=
, k = 0, +/-1, +/-2, . . . or
=
, k = 0, +/-1, +/-2, . . .
Thus there are two sets of solutions:
1. x =
=
, which is equivalent to x =
,
and the other family
2. x =
=
Answer. There are two sets of solutions: 1) x =
and 2) x =
, k = 0, +/-1, +/-2, . . .
The plot below confirms these solutions.
Plots y =
and y = 1